Science:Math Exam Resources/Courses/MATH110/April 2019/Question 04 (a)
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Question 04 (a) 

Suppose the variables and are related by the equation
Find . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Take the derivative of both sides of the equation with respect to and then solve for .

Hint 2 

To compute the derivatives, treat as a function of and use the chain rule every time you need to take its derivative. For example, . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The procedure is to take the derivative with respect to of both sides of the equation and then solve for .
The right hand side of the equation above is zero because 32 is a constant. To compute the left hand side, treat y as a function of x and use the chain rule every time you need to take its derivative:
Solving for gives the result
